Encoding phylogenetic trees in terms of weighted quartets
For a finite set X, an edge-weighted phylogenetic X -tree, or phylogenetic tree for short, is a tree T having leaf set X and no degree 2 vertices, together with a map from the edge set of T to ℝ≥₀. Within the field of phylogenetics, several methods have been proposed for constructing such trees (where X is usually a set of species) that work by trying to piece together quartet trees on X, i.e. edge-weighted phylogenetic Y-trees with Y ⊆ X and IYI = 4. Thus it is of interest to characterise when a collection of quartet trees corresponds to a (unique) phylogenetic tree. Recently, Dress and Erdös provided such a characterisation for binary phylogenetic trees, that is, phylogenetic trees all of whose internal vertices have degree 3. Here we provide a new characterisation for arbitrary phylogenetic trees.
SubjectsField of Research::01 - Mathematical Sciences::0102 - Applied Mathematics::010202 - Biological Mathematics
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